01 GDC08 Eiserloh Squirrel Physics Overview

8/4/2019 01 GDC08 Eiserloh Squirrel Physics Overview

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Physics for Games ProgrammersProblem Overview

Squirrel Eiserloh

Technical DirectorMumboJumbo Games

[email protected]
mailto:[email protected]://www.algds.org/http://www.algds.org/mailto:[email protected]


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Types of Problems

Knowing when to cheat

Simplifying things

Giving shape to things

Moving things around Simulation baggage

Detecting (and resolving) collisions

Sustained interactions Dealing with the impossible

Making it fast enough


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Knowing When To Cheat


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Knowing When to Cheat

Discrete physics simulation fallsembarrassingly short of reality.

Real physics is prohibitively expensive...

...so we cheat. We need to cheat enough to be able to

run in real time.

We need to not cheat so much that things

break in a jarring and unrecoverable way. Much of the challenge is knowing how and

when to cheat.


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Knowing When to Cheat

Ask:

Will the player notice?

Will the player care?

Will the results be predictable?

Are we at least cheating in a consistent way?

Will the simulation break? If the simulation breaks, they will notice and theywill care

Some crimes are greater than others


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Simplifying Things


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Simplifying Things

Simplified bodies


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Simplifying Things

Simplified bodies

Even more simplifiedbodies


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Simplifying Things

Simplified bodies


Convex bodies


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Simplifying Things

Simplified bodies


Convex bodies

Homogeneous bodies


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Simplifying Things

Simplified bodies


Convex bodies

Homogeneous bodies

Rigid bodies


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Simplifying Things

Simplified bodies


Convex bodies

Homogeneous bodies

Rigid bodies

Indestructible bodies


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Simplifying Things

Movement is oftenassumed to be in avacuum (ignoring air

resistance)


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Simplifying Things

Movement is oftenassumed to be in avacuum (ignoring air

resistance)

Even when airresistance doesget

simulated, it is hugelyoversimplified


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Simplifying Things

Collisions are oftenassumed to be perfectand elastic

That is, 100% of theenergy before thecollision is maintained

after the collision

Think billiard balls


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Giving Shape to Things


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N-sphere

2d: Disc

3d: Sphere


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N-sphere

2d: Disc

3d: Sphere

Simplex

2d: Triangle

3d: Tetrahedron


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N-sphere

2d: Disc

3d: Sphere

Simplex

2d: Triangle

3d: Tetrahedron

Convex Polytope

2d: Convex Polygon

3d: Convex Polyhedron

a.k.a. Convex Hull

a.k.a. Brush (Quake)


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Discrete OrientedPolytope (DOP)


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Oriented BoundingBox (OBB)


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Axis-Aligned BoundingBox (AABB)


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Capsule


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Capsule

Cylinder (3d only)


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Moving Things Around


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Moving Things Around Kinematics

Describesmotion

Uses position, velocity,momentum,

acceleration


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Describesmotion


acceleration Dynamics

Explainsmotion

Uses forces

...and impulses


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Describesmotion


acceleration Dynamics

Explainsmotion

Forces (F=ma)

Impulses

Rotation

Torque

Angular momentum

Moment of inertia


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How to compute thenext position andvelocity from current

position and velocity? This process is called

integration;

An algorithm for doing

this in an integrator


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integration;




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integration;




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integration;



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integration;



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integration;


this in an integrator Which integration

method to use?

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integration;



method to use?

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integration;



method to use?

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integration;



method to use?

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integration;



method to use?

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Simulation Baggage

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Simulation Baggage

Flipbook syndrome

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Simulation Baggage

Flipbook syndrome

Things can happenin-between snapshots

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Simulation Baggage

Flipbook syndrome

Things mostlyhappenin-between snapshots

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Simulation Baggage

Flipbook syndrome


Curved trajectoriestreated as piecewiselinear

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Simulation Baggage

Flipbook syndrome


Curved trajectoriestreated as piecewiselinear

Terms often assumed

to be constantthroughout the frame

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Simulation Baggage (contd)

Error accumulates

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Error accumulates

Energy is not alwaysconserved

Energy loss can beundesirable

Energy gain is evil

Simulations explode!

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Error accumulates



Energy gain is evil


Rotations are often

assumed to happeninstantaneously atframe boundaries

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Error accumulates



Energy gain is evil


Rotations are often

assumed to happeninstantaneously atframe boundaries

Numerical nightmares!

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Collision Detection

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Collision Detection

We need to determineifAand B intersect

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Collision Detection

We need to determineif A and B intersect

Worse yet, they could

be (and probably are)in motion

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Collision Detection

We need to determineif A and B intersect

Worse yet, they could

be (and probably are)in motion

If they did collide, weprobably also need to

know when theycollided

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Collision Response

...and we need tofigure out how toresolve the collision

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Sustained Interactions

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Surface contact

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Surface contact

Edge contact

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Surface contact

Edge contact

Contact points

Different solutions

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Surface contact

Edge contact

Contact points

Different solutions

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Surface contact

Edge contact

Contact points

Different solutions

Stacking

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Surface contact

Edge contact

Contact points

Different solutions

Stacking

Friction

Static & Kinetic

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Surface contact

Edge contact

Contact points

Different solutions

Stacking

Friction

Static & Kinetic

Constraints & Joints

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Dealing With the Impossible

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Interpenetration

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Interpenetration

Tunneling

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Interpenetration

Tunneling

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Interpenetration

Tunneling

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Interpenetration

Tunneling

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Tunneling(Sucks)

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Tunneling

Small objects tunnel more easily

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Tunneling (contd)

Possible solutions

Minimum size requirement?

Inadequate; fast objects still tunnel

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Tunneling (contd)

Fast-moving objects tunnel more easily

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Tunneling (contd)

Possible solutions

Minimum size requirement?

Inadequate; fast objects still tunnel

Maximum speed limit?

Inadequate; since speed limit is a function of objectsize, this would mean small & fast objects (bullets)would not be allowed

Smaller time step? Helpful, but inadequate; this is essentially the same

as a speed limit

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Tunneling (contd)

Besides, even withmin. size requirementsandspeed limits anda

small timestep, youstill have degeneratecases that causetunneling!

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Tunneling (contd)



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Tunneling (contd)



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Tunneling (contd)



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Tunneling (contd)

Tunneling is very, very bad this is not amundane detail

Things falling through world

Bullets passing through people or walls

Players getting places they shouldnt

Players missing a trigger boundary

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Tunneling (contd)

Interpenetration

Tunneling

Rotational tunneling

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Making It Fast Enough

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Dont be too particulartoo soon

Avoid unnecessary

work

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Avoid unnecessary

work Eschew n-squared

operations

Avoid the everythingvs. everything case

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Avoid unnecessary

work Eschew n-squared

operations

Avoid the everythingvs. everything case

Try using simulationislandsand spacepartitioning to divideand conquer

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Simulation Islands

Consider:

1000 objects, 1 island

1000x1000 checks

= 1 Million checks

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Simulation Islands

Consider:

1000 objects, 1 island

1000x1000 checks

= 1 Million checks Verses:

1000 objects, dividedinto 10 islands of 100

10 x (100x100) checks

= 100,000 checks

1/10th as many!

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Simulation Islands

Simulation islands cango to sleep whenthey become stable

i.e. when forces andmotion remainunchanged

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Simulation Islands



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Simulation Islands



When an object entersthe islands bounds...

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Simulation Islands




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Simulation Islands




...the island wakes up

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Simulation Islands

Add the newcomer tothis simulation island

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Simulation Islands

Add the newcomer tothis simulation island

...and put it back to

sleep once it stabilizes

This is just one ofmany ways to reduce

complexity

Well be coveringseveral others later on

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Can also exploit work previously done

Make educated assumptions using: Temporal / frame coherence:Things tend not

to have changed a whole lot in the 15ms or sosince the previous frame, so save the previousframes results!

Spatial coherence:Things tend to miss each

other far more often than they collide, andonly things in the same neighborhood cancollide with each other

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Summary

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Summary

The nature of simulation causes us realproblems... problems which cant beignored

So we cheatAnd we simplify things

And even then, it can get quite complex...

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Summary (contd)

Problems were concerned with: How should we choose to represent physical bodies?

How should we simulate and compute motion?

How can we prevent energy build-up?

How do we cope with floating point error? How can we detect collisions especially when large

numbers of objects are involved?

How can we prevent tunneling?

How should we resolve penetration?

How should we handle contact?

How do we deal with non-rigid bodies?

How can we relieve CPU burden?

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Questions?

Feel free to reach me by email at:

[email protected]
mailto:[email protected]:[email protected]

Documents

01 GDC08 Eiserloh Squirrel Physics Overview